Re: Solutions that are not solutions

*To*: mathgroup at smc.vnet.net*Subject*: [mg32184] Re: [mg32049] Solutions that are not solutions*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Fri, 4 Jan 2002 05:04:01 -0500 (EST)*References*: <200112210857.DAA25144@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

PSi wrote: > > I'm trying to solve a system as follows: > X={{0,y,z},{y,x,t},{u,v,w}} > A={{1,1,a},{0,1,0},{0,0,1}} > Solve[{X.A==Transpose[A].X, Det[X]==1}, > {x,y,z,t,u,v,w}] > > Mathematica 4.1 gives two solutions: > X1={{0,y,0},{y,x,t},{0,v,-1/y^2}} > and > X2={{0,y,a*y},{y,(a*t*y^2-1+a*v*y^2-w*y^2)/(a*y)^2,t}, > {a*y,v,w}} > > However, X1 is not a solution: > X1.A-Transpose[A].X1={{0,0,0},{0,0,a*y},{0,-a*y,0}} > > Could anybody explain this behaviour? > Thanks > PSi Simpler form: polys = {a*y-z, u-a*y, a*u-a*z, -1+t*u*y-w*y^2-u*x*z+v*y*z}; vars = {x,y,z,t,u,v,w}; InputForm[sol1 = Solve[polys==0, vars, Sort->False]] I use Sort->False so there can be no confusion over which variables should be solved in terms of which. In[6]:= InputForm[sol1 = Solve[polys==0, vars, Sort->False]] Solve::svars: Equations may not give solutions for all "solve" variables. Out[6]//InputForm= {{y -> (-I)/Sqrt[w], z -> 0, u -> 0}, {y -> I/Sqrt[w], z -> 0, u -> 0}, {x -> (-a^2 + a*t*u^2 + a*u^2*v - u^2*w)/(a^2*u^2), y -> u/a, z -> u}} The first two solutions are not generically correct insofar as they force a parameter equation a==0. The fact that these are returned at all is a bug (alas) which will be fixed. Daniel Lichtblau Wolfram Research